What is the smallest positive x satisfying log_{sin x} cos x + log_{cos x} sin x = 2?
A.π/2
B.π/3
C.π/4✓ Correct
D.π/6
Explanation
Let t = log_{sin x} cos x. Then t + 1/t = 2, giving t = 1. So log_{sin x} cos x = 1, meaning cos x = sin x, i.e., tan x = 1. Smallest positive x is π/4.
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